The edge-based strain smoothing method for compressible and nearly incompressible non-linear elasticity for solid mechanics

E-print/Working paper (in press)

Novel deep learning approaches for learning scientific simulations

Scientific Conference (2023, August)

An a posteriori error estimator for the spectral fractional power of the Laplacian

Scientific Conference (2023, June 06)

Fractional powers of the Laplacian operator are important tools in the modeling and study of non-local phenomena. Several numerical challenges arise from the discretization of these operators due to their ... [more ▼]

Fractional powers of the Laplacian operator are important tools in the modeling and study of non-local phenomena. Several numerical challenges arise from the discretization of these operators due to their non-local nature. For example, a direct discretization via finite element methods can lead to dense and possibly large linear systems. One way to circumvent this density is by using a rational scheme combined with a finite element method. In this talk we describe a novel local a posteriori estimator for the finite element discretization error measured in the L2 norm that can be used to perform adaptive mesh refinement. This estimator is adapted from the strategy introduced by Bank and Weiser and can be used with any rational approx- imation scheme such as best uniform rational approximations or schemes based on the Dunford–Taylor formula. Especially, our estimator preserves the locality and robustness of the Bank–Weiser estimator and preserves the parallel nature of rational approximations. In addition, oour method can be combined with an estimator for the rational approximation error to obtain a more complete description of the discretization errors. Finally, we use an implementation in the FEniCSx finite element software to demonstrate the performances of our method on several numerical experiments including three–dimensional prob- lems. [less ▲]

MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations

E-print/Working paper (2023)

In many cutting-edge applications, high-fidelity computational models prove too slow to be practical and are thus replaced by much faster surrogate models. Recently, deep learning techniques have become ... [more ▼]

In many cutting-edge applications, high-fidelity computational models prove too slow to be practical and are thus replaced by much faster surrogate models. Recently, deep learning techniques have become increasingly important in accelerating such predictions. However, they tend to falter when faced with larger and more complex problems. Therefore, this work introduces MAgNET: Multi-channel Aggregation Network, a novel geometric deep learning framework designed to operate on large-dimensional data of arbitrary structure (graph data). MAgNET is built upon the MAg (Multichannel Aggregation) operation, which generalizes the concept of multi-channel local operations in convolutional neural networks to arbitrary non-grid inputs. The MAg layers are interleaved with the proposed novel graph pooling/unpooling operations to form a graph U-Net architecture that is robust and can handle arbitrary complex meshes, efficiently performing supervised learning on large- dimensional graph-structured data. We demonstrate the predictive capabilities of MAgNET for several non-linear finite element simulations and provide open-source datasets and codes to facilitate future research. [less ▲]

An a posteriori error estimator for the spectral fractional power of the Laplacian

in Computer Methods in Applied Mechanics and Engineering (2023), 407

We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes ... [more ▼]

We develop a novel a posteriori error estimator for the L2 error committed by the finite ele- ment discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi–discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non–fractional parametric problems. The estimator involves applying the implicit Bank–Weiser error estimation strategy to each parametric non–fractional problem and reconstructing the fractional error through the same rational approximation used to compute the solution to the original fractional problem. We provide several numerical examples in both two and three-dimensions demonstrating the effectivity of our estimator for varying fractional powers and its ability to drive an adaptive mesh refinement strategy. [less ▲]

SOniCS: Interfacing SOFA and FEniCS for advanced constitutive models

Scientific Conference (2022, August)

The Simulation Open Framework Architecture (SOFA) is a software environment for building simulations with a particular focus on real-time medical applications, e.g. surgery. Its scope is far broader than ... [more ▼]

The Simulation Open Framework Architecture (SOFA) is a software environment for building simulations with a particular focus on real-time medical applications, e.g. surgery. Its scope is far broader than the FEniCS Project, encompassing e.g. rigid body dynamics, interfacing with haptic devices, contact and visualisation. Naturally, it also includes some finite element models of soft tissue mechanics, but these capabilities are currently ‘pre-baked’ and limited to a few simple constitutive models. The goal of this work is to incorporate state-of-the-art code generation tools from the FEniCS Project into SOFA in order to hugely increase SOFA’s capabilities in terms of soft tissue mechanics. To this end we have developed a new SOFA plugin named SOniCS. For adding a new material model in SOniCS, the user describes its strain energy density function using UFL (Unified Form Language) syntax. Then, using FFCx (FEniCSx Form Compiler) we generate the C code associated with the kernels corresponding to the automatically differentiated cell-local residual and stiffness forms. Finally, we assemble these kernels in SOFA into global tensors and solve the resulting non-linear systems of equations. The result is that it is now possible to straightforwardly implement complex material models such as the Holzapfel-Ogden anisotropic model into SOFA, and to use them alongside SOFA’s existing strong feature set in medical simulation. [less ▲]

Towards real-time patient-specific breast simulations: from full-field information to surrogate model

Scientific Conference (2022, July)

In breast cancer treatment, surgery is one of the most common practices [DeSantis et al., 2019]. The surgery involves a complex pipeline, principally due to the difference between the imaging and the ... [more ▼]

In breast cancer treatment, surgery is one of the most common practices [DeSantis et al., 2019]. The surgery involves a complex pipeline, principally due to the difference between the imaging and the surgical posture [Mazier et al., 2021]. Indeed, because of the stance difference, the surgeon has to rely on radioactive or invasive markers to predict the tumor position in the surgical setup. Biomechanical simulations could predict such complex tumor displacements but often require patient-specific data (material properties, organs geometries, or loading and boundary conditions). Full-field acquisitions coupled with landmark identifications allow obtaining relative deformation between the different configurations. Having this information and assuming a finite element model, an identification procedure of the model parameters can be carried out. Finally, finding a suitable computational model allowing for a compromise between accuracy and speed, one may consider surrogate models for real-time simulations (20 to 50 FPS). In this work, we obtained the patient-specific geometry through micro-computed tomography in 8 different configurations, including 15 bio-markers. Assessing the displacement of the bio-markers enabled us to infer the relative strains between the different configurations. A heterogeneous neo-Hookean model was assumed for simulating soft tissue behavior. Based on the displacements and the position of the biomarkers, model parameters identification was performed to calibrate the experimental data with the finite element method results. To overcome speed performance issues, Convolutional Neural Network (CNN) trained with a synthetic simulation-based dataset generated by applying different gravity directions is used. Preliminary results show that CNN can predict the displacement of anatomical landmarks to millimetric precision and is 100 times faster than the finite element method, satisfying our real-time objective. Plus, the use of Bayesian inferences involves a longer prediction time but allows a 95% confidence interval of the biomarkers' displacements. For a given precision, contrary to CNNs, optimization methods are computationally expensive and depend on an initialization point. Although CNNs require new training for each patient, optimization algorithms can be applied regardless of the patient's geometry. Through this study, we observed that material properties were playing an essential role but not as much as the anatomical structures e.g. infra-mammary or Copper’s ligaments. [less ▲]

Real-Time Large Deformation Simulations Using Probabilistic Deep Learning Framework

Poster (2022, June 28)

Imaging-informed BIOmechanical brain tumor forecast MOdelling

Scientific Conference (2022, June 06)

Grade 3 and 4 Astrocytomas are high grade gliomas (HGG) that usually result from initially less aggressive low grade gliomas (LGG) through malignant transformation (MT). This process has various ... [more ▼]

Grade 3 and 4 Astrocytomas are high grade gliomas (HGG) that usually result from initially less aggressive low grade gliomas (LGG) through malignant transformation (MT). This process has various definitions in the literature, clinical and histopathological, depending on the scale of the study and researchers' interest. We introduce an overview of different aspects of MT: molecular, clinical and the role of the microenvironment in acquiring the malignant phenotype. Furthermore, we introduce a new hypothesis that could explain the spatial progression of low grade astrocytoma (LGA) during MT. The former hypothesis will next be tested on LGA patients through tumor segmentation from Medical Resonance Images (MRI) and a mechanistic growth model. [less ▲]

Real-time large deformations: A probabilistic deep learning approach

in The 8th European Congress on Computational Methods in Applied Sciences and Engineering (2022, June)